We describe the design of the linear motion stage for a Variable-delay Polarization Modulator (VPM) and of a grid flattener that has been built and integrated into the Hertz ground-based, submillimeter polarimeter. VPMs allow the modulation of a polarized source by controlling the phase difference between two linear, orthogonal polarizations. The size of the gap between a mirror and a very flat polarizing grid determines the amount of the phase difference. This gap must be parallel to better than 1% of the wavelength. A novel, kinematic, flexure-based mechanism is described that passively maintains the parallelism of the mirror and the grid to 1.5 pm over a 150 mm diameter, with a 400 pm throw. A single piezoceramic actuator is used to modulate the gap, and a capacitive sensor provides position feedback for closed-loop control. A simple device that ensures the planarity of the polarizing grid is also described. Engineering results from the deployment of this device in the Hertz instrument April 2006 at the Submillimeter Telescope Observatory (SMTO) in Arizona are presented.